(picks up the chalk)
I believe fervently that, in the 2D image space, this rotation to grad is useful:
M = M (no rotation)
a = 0,90,180,270,360 degrees, or [0,360]degress
1 N = 2dcfft(M); the elements are cos and sin, recall that?
2 O = e^-ia(M); element by element component rotation, ok?
3 P = 2dicfft(O); image reformation. (offers chalk, no takers)
Note for a = 0, or 360 degrees, P = M to computational accuracy.
So, WTF happens between? Well, it's all about the pencilsketch and modeling for artclasses. I do that. And in the studio I hold still, shut TF up, and *think* about the brain dynamics.
In between:
At a = 90, O = |grad(M)|
The other angles are left as an exercise for the interested reader!
Cheers from Dana at Replikon Dot Net  Mathcad 6.0 Plus! (chalk returned)